Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26028698 | C2 | semidirect |
| 3. #26020195 | C2 | semidirect |
| 4. #26018768 | C2 | semidirect |
| 5. #26018128 | C2 | semidirect |
| 6. #26018098 | C2 | semidirect |
| 7. C89×#1471 | C2 | semidirect |
| 9. C22×#13083562 | C4 | semidirect |
| 10. C22×#13083559 | C4 | semidirect |
| 18. C2×#15667935 | C4 | semidirect |
| 19. C2×#15667932 | C4 | semidirect |
| 286. #1471 | D89 | semidirect |
| 289. C89 | #9241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151741 | 2 |
| #26028698 | 2 |
| #26020195 | 2 |
| #26018768 | 2 |
| #26018128 | 2 |
| #26018098 | 2 |
| C89×#1471 | 2 |
| #9241 | 89 |